超声衍射层析成像的高精度核卷积插值重建算法

方杰 1; 2; 韦穗 1; 霍修坤 1

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超声衍射层析成像的高精度核卷积插值重建算法

更新时间：2025-07-09

- 超声衍射层析成像的高精度核卷积插值重建算法
- An Accurate Reconstruction Algorithm in Diffraction Ultrasound Tomography Using Kernel Convolution Interpolation
- 西安交通大学学报 2009年43卷第10期页码：94-98
- 作者机构：
  
  1. 安徽大学安徽省现代成像与显示技术重点实验室,合肥,230039
  2. 皖西学院机械与电子工程系,安徽,六安,237009
- 作者简介：
- 基金信息：
  
  : 2008-11-20. 作者简介: 方杰(1978-),男,博士生;韦穗(联系人),女,教授,博士生导师. 基金项目: 国家自然科学基金资助项目(60603083);安徽省优秀青年人才基金资助项目(2008jq1156);教育部高等学校博士学科点专项科研基金资助项目(20070357003).
- DOI：
  中图分类号： TN911.72
- 网络首发：2009-10-10，
  
  纸质出版：2009
- 稿件说明：
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方杰 1, 2, 韦穗 1, 等. 超声衍射层析成像的高精度核卷积插值重建算法[J]. 西安交通大学学报, 2009,43(10):94-98.

An Accurate Reconstruction Algorithm in Diffraction Ultrasound Tomography Using Kernel Convolution Interpolation[J]. 2009, 43(10): 94-98.
方杰 1, 2, 韦穗 1, 等. 超声衍射层析成像的高精度核卷积插值重建算法[J]. 西安交通大学学报, 2009,43(10):94-98. DOI：

An Accurate Reconstruction Algorithm in Diffraction Ultrasound Tomography Using Kernel Convolution Interpolation[J]. 2009, 43(10): 94-98. DOI：

摘要

针对超声衍射层析成像传统采用的双线性插值法重建精度不高的问题

提出一种高精度的核卷积插值重建算法.首先

根据标准的sheep and Logan体模算出重建数据点的值

再选用最小二乘非均匀快速傅里叶变换(LS-NUFFT)算法里的核矩阵作为卷积核

并用此核矩阵将非笛卡儿分布的重建数据点插值到笛卡儿网格内

最后用二维的傅里叶逆变换完成图像的重建.与双线性插值法和高斯核卷积法相比较

LS-NUFFT核矩阵法所得重建图像的2-范数误差比双线性法减少了40%以上

重建时间比高斯核卷积法减少约50%.

Abstract

To overcome the shortage of the conventional bilinear method in diffraction ultrasound tomography reconstruction

an accurate reconstruction algorithm is proposed by using kernel convolution interpolation. The first step of the algorithm calculates the reconstruction data by Shepp and Logan

and the kernel matrix obtained in the least squares nonuniform fast Fourier transform(LS-NUFFT)algorithm is used for the convolution kernel. Then the kernel matrix is used to interpolate the non-Cartesian sampling reconstruction data into the Cartesian grid.The image reconstruction is finally fulfilled by 2-dimensional IFFT. Comparisons with the bilinear method and the Gauss kernel convolution method show that

the reconstruction error in 2-norm is reduced more 40% than the bilinear method

and that the reconstruction time is shortened about 50% compared with the Gauss kernel convolution method.

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references

KAK A C, SLANEY M. Principles of computerized tomographic imaging [M]. New York, USA: Society ofIndustrial and Applied Mathematics,2001.

BRONSTEIN M M, BRONSTEIN A M, AZHAI H. Reconstruction in diffraction ultrasound tomography using nonuniform FFT [J]. IEEE Trans on Med Imaging, 2002, 21(11): 1395-1401.

ZHANG Dongwen, TAO Jinxu.A novel gridding algorithm using NUFFT with applications to ultrasound diffraction tomography [C]∥Proceedings of the 2nd International Conference on Bioinformatics and Biomedical Engineering. Piscataway, NJ, USA:IEEE, 2008: 2473-2476.

Dutt A, ROKHLIN V. Fast Fourier transforms for nonequispaced data[J]. SIAM Journal on Scientific Computing, 1993, 14(6):1368-1393.

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SHA Liewei, GUO Hua, SONG Anwen. An improved gridding method for spiral MRI using nonuniform fast Fourier transforms[J]. Journal of Magnetic Resonance, 2003, 162(2): 250-258.

FESSLER J A. On NUFFT-based gridding for non-Cartesian MRI [J]. Journal of Magnetic Resonance, 2007, 188(1): 191-195.

SONG Jiayu, LIU Qinhua. Improving non-Cartesian MRI reconstruction through discontinuity subtraction [J].International Journal of Biomedical Imaging, 2006, 1(2): 1-9.

RASHE V, PROKSA R, SINKUS R, et al. Resampling of data between arbitrary grids using convolution interpolation [J]. IEEE Trans on Med Imaging, 1999, 18(5): 385-392.

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